Inner Solar System
An $N$-body gravitational model of the inner solar system (Sun and the terrestrial planets), governed by the Hamiltonian
\[H(q, p) = \sum_i \frac{\| p_i \|^2}{2 m_i} - G \sum_{i < j} \frac{m_i m_j}{\| q_i - q_j \|} .\]
This system is documented for completeness but is not yet provided as a problem type in GeometricProblems.jl. For a small gravitational $N$-body example, see the Three Body Problem.